Optical Near-field Electron Microscopy

New Paper on "Fundamental bounds on the precision of iSCAT, COBRI and dark-field microscopy for 3D localization and mass photometry""


Our new paper compares the estimation precision concerning mass photometry and particle tracking that is achievable using interferometric imaging schemes (iScat, COBRI, Dark-field).

Interferometric imaging is an emerging technique for particle tracking and mass photometry. Mass or position are estimated from weak signals, coherently scattered from nanoparticles or single molecules, and interfered with a co-propagating reference. In this work, we perform a statistical analysis and derive lower bounds on the measurement precision of the parameters of interest from shot-noise limited images. This is done by computing the classical Cramér–Rao bound (CRB) for localization and mass estimation, using a precise vectorial model of interferometric imaging techniques. We then derive fundamental bounds valid for any imaging system, based on the quantum Cramér–Rao formalism. This approach enables a rigorous and quantitative comparison of common techniques such as interferometric scattering microscopy (iSCAT), coherent brightfield microscopy, and dark-field microscopy. In particular, we demonstrate that the light collection geometry in iSCAT greatly increases the axial position sensitivity, and that the Quantum CRB for mass estimation yields a minimum relative estimation error of , where N is the number of collected scattered photons.


Jonathan Dong, Dante Maestre, Clara Conrad-Billroth and Thomas Juffmann,
Fundamental bounds on the precision of iSCAT, COBRI and dark-field microscopy for 3D localization and mass photometry
Journal of Physics D: Applied Physics 54, 39 (2021).


view full article: here




Cramér–Rao bounds for mass estimation, as a function of zf for iSCAT (cyan), COBRI (blue), and Darkfield (black). The dotted line gives the CRB for the joint estimation of mass and zp position in iSCAT. The CRBs are normalized by the mass to present relative precision. QCRBs correspond to the horizontal dashed lines, they do not depend on the imaging geometry. The particle is sitting on the coverslip at zp = 5 nm.